基于二阶锥规划无标定参照物的手眼标定

Hand-eye calibration method without a calibration reference based on second-order cone programming

为了克服传统机器人手眼标定方法求解手眼关系及机器人坐标系与世界坐标系方位关系对标定参照物的依赖,提出一种基于二阶锥规划的无标定参照物手眼标定改进方法,并搭建相关实验系统进行验证。首先,利用运动恢复结构算法解算定义在一个尺度因子基础上的相机运动矩阵;然后,引入对偶四元数理论参数化标定方程中的旋转矩阵和平移向量;最后,通过二阶锥规划方法同时求解相机运动矩阵尺度因子、手眼关系及机器人坐标系与世界坐标系方位关系的最优解。仿真和实测结果表明,在没有标定参照物作为测量基准的情况下,标定结果中旋转参数相对误差为3.998%,平移参数相对误差为0.117%。与其他标定方法相比,该方法提高了无标定参照物模式下机器人手眼标定精度,扩展了手眼标定方法的应用范围。

In order to overcome the restrictions of traditional hand-eye methods for determining hand-eye correspondence and robot-world orientation with a calibration reference,an improved hand-eye calibration approach without a calibration reference is proposed based on second-order cone programming.A relevant experimental system is established for its validation.First,a structure-from-motion approach is used to recover the camera motion matrix up to scaling.Then,the rotation and translation matrix in the calibration equation is parameterized by dual quaternion theory.Finally,the second-order cone programming method is used to simultaneously determine the optimal solution for the scale factor of the camera motion matrix,the robot-world calibration and the hand-eye calibration.Both the simulation and experimental results indicate that,for the calibration precision,the relative error of rotation is 3.998%and the relative error of translation is 0.117%in the absence of a calibration reference as a benchmark.Compared with other calibration methods,the proposed method can effectively improve the accuracy of robot-world calibration and hand-eye calibration without a reference,and extend the range of applications of the hand-eye calibration method.